The Critical Exponent is Computable for Automatic Sequences

The critical exponent of an infinite word is defined to be the supremum of the exponent of each of its factors. For k-automatic sequences, we show that this critical exponent is always either a rational number or infinite, and its value is computable. Our results also apply to variants of the critical exponent, such as the initial critical exponent of Berthe, Holton, and Zamboni and the Diophantine exponent of Adamczewski and Bugeaud. Our work generalizes or recovers previous results of Krieger and others, and is applicable to other situations; e.g., the computation of the optimal recurrence constant for a linearly recurrent k-automatic sequence.Comment: In Proceedings WORDS 2011, arXiv:1108.341

Something\u27s Gotta Give: Bent Rules, Breached Bottom Line, and the International Amateur Athletics Federations\u27 Handling of the China Question

International Sport Federations (IFs), as part of the Olympic network, have different organisational structures and decision-making mechanisms from the International Olympic Committee (IOC). The authors, in examining the history of the International Amateur Athletics Federations’ (IAAF) handling of the “China question” in international sport, probe how these differences translated into the IAAF’s organisational politics and power dynamics in face of governmental interference. Primarily examining archival documents obtained from the IAAF Archive and the IOC Historical Archives, the authors particularly follow how the self-governing IAAF upheld, bent, and modified its statutes during its engagement with the People’s Republic of China (PRC) from the 1950s to the 1970s and around its eventual admission of the PRC’s Athletics Association in 1978. It is also argued that the IAAF’s engagement and inclusion of the PRC allowed the consolidation of its monopolising power in global athletics governance

Nondispersive solutions to the L2-critical half-wave equation

We consider the focusing $L^2$-critical half-wave equation in one space dimension $$i \partial_t u = D u - |u|^2 u,$$ where $D$ denotes the first-order fractional derivative. Standard arguments show that there is a critical threshold $M_* > 0$ such that all $H^{1/2}$ solutions with $\| u \|_{L^2} < M_*$ extend globally in time, while solutions with $\| u \|_{L^2} \geq M_*$ may develop singularities in finite time. In this paper, we first prove the existence of a family of traveling waves with subcritical arbitrarily small mass. We then give a second example of nondispersive dynamics and show the existence of finite-time blowup solutions with minimal mass $\| u_0 \|_{L^2} = M_*$. More precisely, we construct a family of minimal mass blowup solutions that are parametrized by the energy $E_0 >0$ and the linear momentum $P_0 \in \R$. In particular, our main result (and its proof) can be seen as a model scenario of minimal mass blowup for $L^2$-critical nonlinear PDE with nonlocal dispersion.Comment: 51 page

Lesbian and bisexual women's experiences of sexuality-based discrimination and their appearance concerns

Lesbian and bisexual women frequently experience sexuality-based discrimination, which is often based on others' judgements about their appearance. This short article aims to explore whether there is a relationship between lesbian and bisexual women's experiences of sexuality-based discrimination and their satisfaction with the way that they look. Findings from an online survey suggest that discrimination is negatively related to appearance satisfaction for lesbian women, but not for bisexual women. It is argued that this difference exists because lesbian appearance norms are more recognisable and distinctive than bisexual women's appearance norms

The effects of socioeconomic status and indices of physical environment on reduced birth weight and preterm births in Eastern Massachusetts

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Background: Air pollution and social characteristics have been shown to affect indicators of health. While use of spatial methods to estimate exposure to air pollution has increased the power to detect effects, questions have been raised about potential for confounding by social factors.Methods: A study of singleton births in Eastern Massachusetts was conducted between 1996 and 2002 to examine the association between indicators of traffic, land use, individual and area-based socioeconomic measures (SEM), and birth outcomes ( birth weight, small for gestational age and preterm births), in a two-level hierarchical model.Results: We found effects of both individual ( education, race, prenatal care index) and area-based ( median household income) SEM with all birth outcomes. The associations for traffic and land use variables were mainly seen with birth weight, with an exception for an effect of cumulative traffic density on small for gestational age. Race/ethnicity of mother was an important predictor of birth outcomes and a strong confounder for both area-based SEM and indices of physical environment. The effects of traffic and land use differed by level of education and median household income.Conclusion: Overall, the findings of the study suggested greater likelihood of reduced birth weight and preterm births among the more socially disadvantaged, and a greater risk of reduced birth weight associated with traffic exposures. Results revealed the importance of controlling simultaneously for SEM and environmental exposures as the way to better understand determinants of health.This work is supported by the Harvard Environmental Protection Agency (EPA) Center, Grants R827353 and R-832416, and National Institute for Environmental Health Science (NIEHS) ES-0002

Do topology and ferromagnetism cooperate at the EuS/Bi2_2Se3_3 interface?

We probe the local magnetic properties of interfaces between the insulating ferromagnet EuS and the topological insulator Bi$_2$Se$_3$ using low energy muon spin rotation (LE-$\mu$SR). We compare these to the interface between EuS and the topologically trivial metal, titanium. Below the magnetic transition of EuS, we detect strong local magnetic fields which extend several nm into the adjacent layer and cause a complete depolarization of the muons. However, in both Bi$_2$Se$_3$ and titanium we measure similar local magnetic fields, implying that their origin is mostly independent of the topological properties of the interface electronic states. In addition, we use resonant soft X-ray angle resolved photoemission spectroscopy (SX-ARPES) to probe the electronic band structure at the interface between EuS and Bi$_2$Se$_3$. By tuning the photon energy to the Eu anti-resonance at the Eu $M_5$ pre-edge we are able to detect the Bi$_2$Se$_3$ conduction band, through a protective Al$_2$O$_3$ capping layer and the EuS layer. Moreover, we observe a signature of an interface-induced modification of the buried Bi$_2$Se$_3$ wave functions and/or the presence of interface states

Exact-exchange density-functional theory for quasi-two-dimensional electron gases

A simple exact-exchange density-functional method for a quasi-two-dimensional electron gas with variable density is presented. An analytical expression for the exact-exchange potential with only one occupied subband is provided, without approximations. When more subbands are occupied the exact-exchange potential is obtained numerically. The theory shows that, in contradiction with LDA, the exact-exchange potential exhibits discontinuities and the system suffers a zero-temperature first-order transition each time a subband is occupied. Results suggesting that the translational symmetry might be spontaneously broken at zero temperature are presented. An extension of the theory to finite temperatures allows to describe a drop in the intersubband spacing in good quantitative agreement with recent experiments.Comment: 14 pages, 3 figure

Parameterized optimized effective potential for atoms

The optimized effective potential equations for atoms have been solved by parameterizing the potential. The expansion is tailored to fulfill the known asymptotic behavior of the effective potential at both short and long distances. Both single configuration and multi configuration trial wave functions are implemented. Applications to several atomic systems are presented improving previous works. The results here obtained are very close to those calculated in either the Hartree-Fock and the multi configurational Hartree-Fock framework.Comment: 8 pages, 3 figure

Large closed queueing networks in semi-Markov environment and its application

The paper studies closed queueing networks containing a server station and $k$ client stations. The server station is an infinite server queueing system, and client stations are single-server queueing systems with autonomous service, i.e. every client station serves customers (units) only at random instants generated by a strictly stationary and ergodic sequence of random variables. The total number of units in the network is $N$. The expected times between departures in client stations are $(N\mu_j)^{-1}$. After a service completion in the server station, a unit is transmitted to the $j$th client station with probability $p_{j}$ $(j=1,2,...,k)$, and being processed in the $j$th client station, the unit returns to the server station. The network is assumed to be in a semi-Markov environment. A semi-Markov environment is defined by a finite or countable infinite Markov chain and by sequences of independent and identically distributed random variables. Then the routing probabilities $p_{j}$ $(j=1,2,...,k)$ and transmission rates (which are expressed via parameters of the network) depend on a Markov state of the environment. The paper studies the queue-length processes in client stations of this network and is aimed to the analysis of performance measures associated with this network. The questions risen in this paper have immediate relation to quality control of complex telecommunication networks, and the obtained results are expected to lead to the solutions to many practical problems of this area of research.Comment: 35 pages, 1 figure, 12pt, accepted: Acta Appl. Mat